# Symbols And Equations, And The Scientific Method

**Symbols and Equations**

We’ve used quite a few symbols so far. Mass represented by m, mass density by the Greek letter rho (r), D means “a change in” a value, and many others. These symbols, which have very specific meanings, are accepted for use by the scientific community. Learning the symbol and its specific meaning is how you learn scientific language.

Symbols are also used in equations, which are mathematical statements in which the quantities (frequently numbers) on one side of the equal sign are equivalent to that on the other side. If the quantities are units, then the units on each side are equivalent. Equations, such as for mass density, are frequently used to describe a property. They can be also used to define a concept, such as the famous equation e = mc2, which presents the concept that mass can be converted to energy (e).

PROPORTIONALITIES can describe how quantities change relative to each other. For example, weight is a VARIABLE quantity that can change in relationship to the amount and type of food consumed. There are 4 different kinds of relationships between variables (see Figure 2). Variables can be directly proportional (one increases, the other then will increase); inversely proportional (one increases, the other decreases); square proportional; or inverse square proportional. Note that the two proportional variables are NOT EQUAL: The proportionality merely describes how they change relative to each other. THEREFORE, A PROPORTIONAL RELATIONSHIP IS NOT AN EQUATION!

For example, the volume of gas you pump at a gas station is directly proportional to the amount of time you pump. The two quantities (volume and time) do not have the same numbers and units, but the two are directly proportional. To make a proportionality statement an equation, a constant value called a PROPORTIONALITY CONSTANT must be applied, as shown in the following formula:

volume gas = (time pumping) (constant)

restated as: V = t x *k* where V = volume t = time *k *= constant

Usually, the constant is given the letter *k*. If we come up with a constant that applies to this situation (let us hypothesize that the pump delivers 10 gallons per minute), we now have an equation (and thus an equality).

gal = (min)(gal/min) min cancel out, so

gal = gal

**The Scientific Method**

The hallmark of any scientific investigation is the accumulation of experimental evidence, namely, the physical evidence that provides explanations for a phenomenon. How is a scientific investigation conducted? One way the scientific method can be presented is depicted in the following steps:

*Observe a phenomenon (some aspect of nature):*Close observation and collection of descriptive measurements about the natural world is an important aspect of all scientific investigations. For example, you might notice that the pond near your favorite golf course has no frogs, even though the farmer’s pond nearby the course has a lot of frogs. Why are there no frogs in the pond at the golf course?*Based on observations, propose an explanation for what is observed.*The potential explanation for the observed phenomenon leads to the formulation of a hypothesis, which is an educated explanation about a phenomenon based on scientific observation. The observation that golf courses use a lot of herbicides, but the farmer uses none (he raises cattle on his farm), might lead you to hypothesize that herbicide run-off into the ponds at the golf course may be toxic to frogs.*Use the explanation to make predictions.*You can make the prediction that ponds with certain levels of herbicides are not going to contain living frogs. Now all you have to do to determine if this is the case is to…*Test the hypotheses by performing an experiment or by making additional observations.*Go to many ponds, some at golf courses, and some on farms using no herbicides. Determine if frogs are present at the ponds, and try to estimate how many. Then determine the herbicide level in each pond.*Modify the original hypothesis based on the results of the experiment.*Do the results support your hypothesis? Refute your hypothesis? Modify you hypothesis to agree with the data, and then…*Retest the modified hypothesis.*

There are many problems with the example given here. What if golf courses use different herbicides? Are they all equally toxic? Is the size of the pond a factor? Is the location (such as near woods or near roads) also a factor? Are certain species of frogs more tolerant of herbicides? Less tolerant? These kind of questions make scientific examinations a long-term process, uncovering layer after layer of complexity to ultimate find a suitable explanation.